Systems, methods and computer program products for modeling costs and profitability of a good

ABSTRACT

Systems, methods and computer program products for determining a learning curve value and modeling an associated profitability of a good are provided. According to one method of determining a learning curve value, recurring costs of producing each unit of the good are modeled as a function of potential learning curve values. Nonrecurring costs of producing each unit of the good are then modeled as a function of potential learning curve values. Next, the learning curve value is determined based upon the recurring costs model and the nonrecurring costs value such that the sum of the recurring costs and nonrecurring costs at the determined learning curve value is minimized over the potential learning curve values.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/453,727, entitled: Systems, Methods and Computer Program Products forModeling Demand, Supply and Associated Profitability of A Good, filedJun. 3, 2003, which is hereby incorporated herein in its entirety byreference.

FIELD OF THE INVENTION

The present invention relates generally to determining a learning curvevalue of a good and, more particularly, to systems, methods and computerprogram products for determining a learning curve value and modelingassociated profitability and costs of a good.

BACKGROUND OF THE INVENTION

In many manufacturing industries today, companies analyze many questionsduring the creation of a manufactured good. Among such questions,companies analyze how much money should be put into research anddevelopment, whether it is best to have a steep learning curve or ashallow learning curve, what is the trade off between recurring costsand nonrecurring costs, should money be spent in lowering the cost ofthe first unit manufactured (referred to as T#1 cost), how much shouldbe invested in automation, and what are the optimum profits. Currently,there are no techniques to adequately answer such questions. Typically,it is left to upper management to gather data and make a judgment callon what it feels is the correct solution. In this regard, for many oldercompanies, a lot of historical data exists that can aid in validatingmost of the decisions.

Of all the questions listed above, the question of what are the optimumprofits is the driving force in business. Every company would like tomaximize their profits. In this regard, profits are a balance betweencosts and revenue. Costs can be divided into two different types,nonrecurring and recurring. Nonrecurring costs are those that areone-time investments that help to start a manufacturing line. Theyinclude the costs of building factories, creating specialized tools(automation), research and development, etc. Recurring costs are thosethat continually (usually annually) need to be invested in to keep amanufacturing line open. They include the costs of materials, buildingmaintenance, worker's salary, etc. The sum of both nonrecurring andrecurring costs are typically referred to as the total cost of aprogram.

In manufacturing and many other fields, recurring costs are usuallylinked to a learning curve. The learning curve describes the level ofimprovement over time. Typically, the learning curve is used to describethe behavior of people who do a job. When trying to build a manufacturedgood for the first time, people will do a job at a given rate. As thesame people continue to do the same job, the quality of their work getsbetter and they can do it at a faster rate. This improvement typicallycontinues as more units are produced. The learning curve, then, is a wayto capture this improvement and factor it into the recurring costs. Inthis regard, recurring costs per unit goes down as more units areproduced. So a learning curve is only relevant when people are integralto a manufacturing line. In the case of a fully automated line, then,the learning curve is flat because there is no improvement over time.

Although it is known that recurring costs drop as time goes on, thelevel that recurring costs begins at is not generally known. However,there is a relationship between the nonrecurring costs and the initiallevel of the recurring costs. To understand why this relationship holds,consider the following simplified example.

As stated before, costs for specialized tools fall under nonrecurringcosts. It is with these tools that people will build a unit of the good.People will be able to do their job faster if they have specializedtools to do the job. They may still be able do the job with lessspecialized tools, but it may take longer. The longer it takes, then,the more it costs to produce the first unit. It is the cost of the firstunit that sets the initial level of the recurring costs. On the otherhand, specialized tools cost money and, therefore, affect thenonrecurring costs. In this regard, a rough inverse relationship can bedrawn from the cost of the first unit (recurring costs) and thenonrecurring costs. In general, as nonrecurring costs go up, the cost ofthe first unit goes down.

Since nonrecurring costs and recurring costs are related, it isdesirable to find the balance between the two that will optimize profitsand, thus, answer the question that is the driving force in business. Itmust be kept in mind, though, that recurring costs change depending onthe learning curve used.

SUMMARY OF THE INVENTION

In light of the foregoing background, embodiments of the presentinvention provide systems, methods and computer program products fordetermining a learning curve value, and modeling associatedprofitability and costs of a good. The systems, methods and computerprogram products of the present invention advantageously are capable ofmodeling the cost of producing the good, including the recurring andnonrecurring costs, while accounting for uncertainty in such costs.Thereafter, the systems, methods and computer program products arecapable of determining a learning curve value to thereby maximizeprofitability. Additionally, the systems, methods and computer programproducts of embodiments of the present invention are capable of modelingthe demand and associated profitability while better accounting for anuncertain market that can be represented by variability in therelationship of the price of the good and the number of units of thegood purchased, as well as the variability in the relationship of thecost of producing the good and an associated learning curve value. Byaccounting for such uncertainty, the systems, methods and computerprogram products of embodiments of the present invention can bettermodel the profitability to thereby maximize such profitability.

According to one aspect of the present invention, a method is providedthat includes determining the learning curve value based upon a model ofprofitability as a function of potential learning curve values, wherethe learning curve value is determined such that the profitability ismaximized over the potential learning curve values. As the learningcurve value is determined based upon a profitability model, the methodcan also include modeling the profitability before determining thelearning curve value mode. In such instances, profitability can bemodeled by also modeling recurring costs to produce the good. Recurringcosts, then, can be modeled by determining a T#1 cost for each of aplurality of potential learning curve values based upon a model of T#1cost as a function of potential learning curve values. Thereafter,recurring costs can be modeled based upon the T#1 cost and a learningcurve for each of the potential learning curve values.

Before determining the T#1 cost, T#1 cost can be modeled as a functionof potential learning curve values. In this regard, T#1 cost can bemodeled by selecting a unit cost to produce the good, and thereafterdetermining a fixed cost to produce a first unit of the good based uponthe unit cost. Then, a variance factor can be determined as a functionof potential learning curve values based upon a variance and a benchmarklearning curve value. After determining the variance factor, T#1 costcan be modeled as a function of potential learning curve values basedupon the variance factor and the fixed cost.

In instances in which the method includes modeling the profitabilitybefore determining the learning curve value, the profitability can bemodeled by further modeling a nonrecurring costs to produce the good.More particularly, nonrecurring costs can be modeled by determining arelationship between nonrecurring costs and potential learning curvevalues. Then, an uncertainty value can be selected from a riskdistribution associated with nonrecurring costs. Thereafter;nonrecurring costs can be modeled based upon the relationship betweennonrecurring costs and potential learning curve values, and theuncertainty value.

In embodiments where profitability is modeled before determining alearning curve value, the profitability can be modeled for each of aplurality of potential learning curve values. Also, in such embodiments,the method can further include forecasting a market by randomlyselecting a predefined number of units of a good based upon a marketpotential distribution. As such, the profitability can be modeled foreach of the plurality of potential learning curve values based upon theforecasted market. The method can include repeatedly forecastingdifferent markets, with profitability being modeled for the plurality ofpotential learning curve values for each of the forecasted markets.Then, a learning curve value can be determined by identifying a learningcurve value for each forecasted market such that the profitability ismaximized over the potential learning curve values, and thereafterdetermining a learning curve value such that the mean profitability ateach identified learning curve value is maximized over the identifiedlearning curve values.

According to another aspect of the present invention, a method isprovided that includes determining a T#1 cost for a selected potentiallearning curve value, and thereafter modeling recurring cost to producea good, in a manner such as described above. The method can also includemodeling T#1 cost, such as in a manner described above. In modeling T#1cost, the method can determine variance by also establishing a pluralityof variance values associated with different learning curve values, andthereafter fitting a curve to define a relationship between theplurality of variance values and associated learning curve values. Alsoin modeling T#1 cost, the method can include repeatedly selectingdifferent unit costs. Thereafter, the method can include modeling therecurring costs for each selected unit cost.

The method according to this aspect can further include forecasting amarket by randomly selecting a predefined number of units of a goodbased upon a market potential distribution. Recurring costs can then bemodeled further based upon the forecasted market. In some instances,such as those in which the good is purchased in a differentiated market,the forecasted market can include a predefined number of contracts eachhaving a predetermined number of units and a predetermined price perunit. In those instances, recurring costs can be modeled further basedupon the predefined number of contracts. In addition to forecasting amarket, the method can include modeling profitability of the good in theforecasted market based upon the recurring costs model and a demandmodel. In some instances, profitability can be modeled further basedupon a nonrecurring costs model. By repeatedly forecasting differentmarkets, recurring costs and profitability can be modeled for each ofthe forecasted markets. Subsequently, recurring costs and profitabilitycan be modeled for a plurality of potential learning curve values foreach forecasted market. As such, a learning curve value can bedetermined by identifying a learning curve value for each forecastedmarket such that the profitability is maximized over the potentiallearning curve values, and thereafter determining a learning curve valuesuch that the mean profitability at each identified learning curve valueis maximized over the identified learning curve values.

According to yet another aspect of the present invention, a method isprovided that includes modeling nonrecurring costs. More particularly,the method includes determining a relationship between nonrecurringcosts and potential learning curve values. For example, the relationshipcan be determined by establishing a plurality of nonrecurring costsvalues associated with different learning curve values, and thereafterfitting a curve to define the relationship between nonrecurring costsvalues and potential learning curve values. After determining arelationship between nonrecurring costs and potential learning curvevalues, an uncertainty value can be selected from a risk distributionassociated with nonrecurring costs. Nonrecurring costs to produce a goodare then modeled based upon the relationship between nonrecurring costsand potential learning curve values, and the uncertainty value. In oneembodiment, for example, the method includes repeatedly selectingdifferent uncertainty values. In this embodiment, the nonrecurring costscan be modeled for each selected uncertainty value.

The method according to this aspect of the present invention can alsoinclude modeling profitability of the good based upon the nonrecurringcosts model, recurring costs model and a demand model. In suchinstances, the method can forecast a market, and thereafter modelprofitability further based upon the forecasted market. Further, themethod can include repeatedly forecasting different markets. As such,the profitability can be modeled for each of the forecasted markets. Themethod can additionally include modeling profitability for a pluralityof potential learning curve values for each forecasted market. As such,a learning curve value can be determined, such as in a manner describedabove.

Advantageously, according to various embodiments of the presentinvention, the determined learning curve value, recurring costs model,nonrecurring costs model and/or profitability are capable of beingmodeled with a processing element operating a spreadsheet softwareprogram. In such embodiments, the determined learning curve value,recurring costs model, nonrecurring costs model and/or profitability canbe presented on a display coupled to the processing element. Moreparticularly, the determined learning curve value can be displayed bypresenting a display of the recurring costs model and the nonrecurringcosts model as functions of potential learning curve values such thatthe determined learning curve value is presented as the potentiallearning curve value that minimizes the sum of the recurring costs andnonrecurring costs. The recurring costs and nonrecurring costs modelscan be presented in a number of manners including, for example, as plotsof different recurring costs and/or nonrecurring costs with associatedpotential learning curve values and/or with associated numbers of unitsof the good in a forecasted market. Similarly, the profitability modelcan be presented, for example, as a plot of different profitability withassociated potential learning curve values and/or with associatednumbers of units of the good in a forecasted market.

Embodiments of the present invention therefore provide systems, methodsand computer program products for determining a learning curve value andmodeling associated profitability and costs of a good. Advantageously,the systems, methods and computer program products of embodiments of thepresent invention are capable of modeling the demand and associatedprofitability while better accounting for variability in therelationship of the price of the good and the number of units of thegood purchased, as well as the variability in the relationship of thecost of producing the good and an associated learning curve value. Assuch, embodiments of the present invention can better model theprofitability to thereby maximize such profitability.

BRIEF DESCRIPTION OF THE DRAWINGS

Having thus described the invention in general terms, reference will nowbe made to the accompanying drawings, which are not necessarily drawn toscale, and wherein:

FIG. 1 is a flowchart including various steps in a system, method andcomputer program product for determining a learning curve valueaccording to one embodiment of the present invention;

FIG. 2 is a flowchart including various steps in a system, method andcomputer program product for modeling the demand for a good purchased ina non-differentiated market according to one embodiment of the presentinvention;

FIG. 3 is a schematic illustration of a price sensitivity distributionrecast in reverse cumulative format utilized during operation of thesystem, method and computer program product of one embodiment of thepresent invention;

FIG. 4 is a schematic illustration of a market penetration distributionfor a forecasted market utilized during operation of the system, methodand computer program product of one embodiment of the present invention;

FIG. 5 is a schematic illustration of a demand curve for a forecastedmarket according to one embodiment of the present invention in thecontext of a good purchased in a non-differentiated market;

FIG. 6 is a schematic illustration of multiple demand curves formultiple forecasted markets according to one embodiment of the presentinvention in the context of a good purchased in a non-differentiatedmarket;

FIG. 7 is a flowchart including various steps in a system, method andcomputer program product for modeling the demand for a good purchased ina differentiated market according to one embodiment of the presentinvention;

FIG. 8 is a graph illustrating a contract purchases collection utilizedduring operation of the system, method and computer program product ofone embodiment of the present invention;

FIG. 9 is a schematic illustration of a demand curve for a forecastedmarket according to one embodiment of the present invention in thecontext of a good purchased in a differentiated market;

FIG. 10A is a flowchart including various steps in a system, method andcomputer program product for modeling recurring costs of a goodaccording to one embodiment of the present invention;

FIG. 10B is a flowchart including various steps in a system, method andcomputer program product for modeling the cost of producing the firstunit (i.e., T#1 cost) of a good according to one embodiment of thepresent invention

FIG. 11 is a schematic illustration of a learning curve associated withthe cost to produce a good utilized during operation of the system,method and computer program product of one aspect of the presentinvention;

FIG. 12 is a schematic illustration of a recurring cost curve utilizedduring operation of the system, method and computer program product ofone aspect of the present invention in the context of a good purchasedin a non-differentiated market;

FIG. 13 is a graph of a cost sensitivity distribution utilized duringoperation of the system, method and computer program product of oneembodiment of the present invention;

FIG. 14A is a graph of variance values and associated learning curvevalues established from theoretical T#1 variance values associated withdifferent learning curve values, utilized to model recurring costs of agood according to one embodiment of the present invention;

FIG. 14B is a graph of a best fit curve established from the variancevalues and associated learning curve values from FIG. 14A;

FIG. 15 is a plot of recurring costs as a function of potential learningcurve values according to one embodiment of the present invention;

FIG. 16 is a schematic illustration of a recurring cost curve utilizedduring operation of the system, method and computer program product ofone embodiment of the present invention in the context of a goodpurchased in a differentiated market;

FIG. 17A is a flowchart including various steps in a system, method andcomputer program product for modeling a nonrecurring costs of a goodaccording to one embodiment of the present invention;

FIG. 17B is a flowchart including various steps in a system, method andcomputer program product for modeling a nonrecurring costs of a goodaccording to another embodiment of the present invention;

FIG. 18A is a graph of nonrecurring costs values and associated learningcurve values utilized to model nonrecurring costs of a good according toone embodiment of the present invention;

FIG. 18B is a graph of a best fit curve established from thenonrecurring costs values and associated learning curve values from FIG.18A;

FIG. 19 is a graph of a risk distribution utilized during operation ofthe system, method and computer program product of one embodiment of thepresent invention;

FIG. 20 is a plot of nonrecurring costs modeled as a function ofpotential learning curve values according to one embodiment of thepresent invention;

FIG. 21 is a schematic illustration comparing the demand curve of FIG. 5with the cost curve of FIG. 12;

FIG. 22 is a schematic illustration of a gross profitability curve and anet profitability curve according to one embodiment of the presentinvention;

FIG. 23 is a plot of gross profitability of a good modeled as a functionof potential learning curve values according to one embodiment of thepresent invention in the context of a good in a non-differentiatedmarket;

FIG. 24 is a plot of net profitability of a good modeled as a functionof potential learning curve values according to one embodiment of thepresent invention in the context of a good in a non-differentiatedmarket;

FIG. 25A is a scatter plot illustrating optimum learning curve valuesagainst the net profitabilities for the respective learning curvevalues, determined according to one embodiment of the present invention;

FIG. 25B is a graph illustrating the mean net profitability for eachpotential learning curve value, determined according to one embodimentof the present invention;

FIG. 26 is a schematic illustration of the market value of a project ofselling a good over time determined according to one embodiment of thepresent invention; and

FIG. 27 is a schematic block diagram of the system of one embodiment ofthe present invention embodied by a computer.

DETAILED DESCRIPTION OF THE INVENTION

The present invention now will be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown. This invention may, however, be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout.

A system, method and computer program product according to one aspect ofthe present invention are provided for determining a learning curvevalue for the manufacture of a good. More particularly, the system,method and computer program product of this aspect are capable ofdetermining a learning curve value that maximizes profits for the saleof the goods in an uncertain future market. Briefly, referring to FIG.1, a method of determining a learning curve value generally begins byforecasting a market of a select size, as shown in block 2. Afterselecting the forecasted market, demand for the good in the forecastedmarket can be modeled, as shown in block 4. Either before, during orafter modeling the demand, a potential learning curve value can beselected from a set of potential learning curve values, as shown inblock 6. Thereafter, recurring costs associated with the manufacture ofthe goods in the forecasted market can be modeled for the selectedpotential learning curve value, as shown in block 8.

After modeling the demand and recurring costs, gross profits for thesale of the good in the forecasted market can be modeled based upon thedemand and recurring costs models, and thereafter a maximum gross profitcan be determined, as shown in block 10. To model net profits for thesale of the good and/or determine the maximum net profit, however,nonrecurring costs associated with the manufacture of the goods are alsomodeled based on the selected potential learning curve value. Thenonrecurring costs can then be added to the recurring costs to determinea total cost to manufacture the good, as also shown in block 8. In suchinstances, net profits for the sale of the good can be modeled basedupon the demand model and the recurring costs model, as well as thenonrecurring costs model, with the maximum net profit being determined,as also shown in block 10.

The process of determining the maximum gross and/or net profits for theforecasted market can continue for all potential learning curves in theset of potential learning curves, as shown in blocks 12, 14. Then, withthe maximum gross and/or net profits for all learning curve values inthe set determined, the gross and/or net profits can be modeled as afunction of learning curve values, as shown in block 16. Thereafter, anoptimal learning curve value can be determined as the learning curvevalue associated with the maximum net profits (or maximum gross profits,if so desired) over all potential learning curve values in the set, asshown in block 18.

Modeling demand, as well as recurring costs, nonrecurring costs andprofits will now be described in more detail.

I. Modeling the Demand for a Good

Modeling the net profitability of the good in a forecasted markettypically begins with modeling the demand of a good, as well as modelingthe associated costs of producing the good. In the economy, products cangenerally be categorized in one of two markets, either anon-differentiated market or a differentiated market. In anon-differentiated market, such as a commodity market, all competinggoods are offered at a single price. For example, wheat, cotton, silverand oil are all goods that are typically offered at a single price. In adifferentiated market, on the other hand, competing goods can bedifferentiated in the features that characterize the respective goods.As such, in a differentiated market, the distinguishing features allowdifferent amounts of goods to be sold at different prices. For example,automobiles and aircraft are both goods that, due to differing features,can be sold at differing prices for differing quantities.

In a non-differentiated market, all goods are typically sold andpurchased according to a single price for each unit of the good. In adifferentiated market, however, the goods can vary in price. In thisregard, goods in a differentiated market are typically sold according tocontracts for a predetermined number of units of the good at apredetermined price for each unit. As such, to more accurately modelprofitability of the good, demand for the good can be modeled for goodsin a non-differentiated market as well as a differentiated market.

A. Goods in Non-Differentiated Markets

The demand for a good in a non-differentiated market is generally afunction of the price per unit of the good and the size of the market interms of the total number of units of the good in the market, both ofwhich differ depending upon the good. In this regard, in modeling thedemand for some subsequent time in the future, neither the price of thegood nor the size of the market can be specified as each includes anamount of uncertainty. Thus, to most accurately model the demand for thegood such that the uncertainty in the price per unit and/or the size ofthe market are captured, the demand is typically modeled based upon adistribution of the possible prices for which the good may be sold, anda distribution of the possible sizes of the market within which the goodmay be sold.

Referring to FIG. 2, modeling the demand for a good in anon-differentiated market generally begins by assessing uncertainty inthe price per unit of the good by determining how the price of the goodaffects whether customers will purchase the good. In this regard,uncertainty in the purchase price of each unit of the good is typicallyexpressed in a price sensitivity distribution of a unit purchase of thegood at a predetermined price, as shown in block 22. The pricesensitivity distribution generally assigns a probability of a unitpurchase to each respective price at which consumers would purchase theunit. The price sensitivity distribution can be expressed according toany of a number of different probability distribution types but, in oneembodiment, the price sensitivity distribution is expressed as alognormal probability distribution. For more information on such a pricesensitivity distribution, as well as modeling the demand and grossprofitability of the good, see U.S. patent application Ser. No.10/453,727 entitled: Systems, Methods and Computer Program Products forModeling Demand, Supply and Associated Profitability of A Good, filedJun. 3, 2003, the contents of which are hereby incorporated by referencein its entirety.

Advantageously, and particularly in instances in which data of real orhypothetical cost data is sparse, uncertainty in the price of the good,or the price sensitivity distribution, can be defined based upon a stateof development of technologies associated with the good. In this regard,in many industries, decisions about projects for the manufacture andsale of a good require manufacturers to estimate technical risk, ortechnical maturity, associated with the state of development of theproject in order to correctly determine success probabilities andinvestment levels for the project, i.e., to determine risk and returnprobabilities. In this regard, development of the project can includeone or more different technologies, with different technologies indifferent stages of development.

Whereas information regarding technical risk can be useful tomanufacturers, such information is often qualitative. For example, onesuch group of qualitative measures of technical risk, or technicalmaturity, are the Technology Readiness Levels (TRL's) developed by theNational Aeronautics and Space Administration (NASA). To account for thestate of development of the associated technologies, each technologyassociated with the good is associated with a qualitative measure ofmaturity, where each qualitative measure of maturity is associated witha distribution. As such, each technology is associated with thedistribution of the respective qualitative measure of maturity.

After associating each technology with the distribution of therespective qualitative measure of maturity, a price point, or moretypically a most likely price, is selected for each technology. A pricedistribution can then be defined for each technology based upon thedistribution associated with the respective qualitative measure ofmaturity and the respective most likely price. A price for eachtechnology can be selected from the cost distributions, such asaccording to a Monte Carlo method, and thereafter summed together to getone possible total price for the good. As known to those skilled in theart, the Monte Carlo method is a method of randomly generating valuesfor uncertain variables to simulate a model. Next, a number of otherprices for each technology can be selected and summed together in asimilar manner to get a number of other possible total prices. From allof the total prices, a mean and standard deviation can be determined tothereby define the price sensitivity distribution. For more informationon such a method of determining the price sensitivity distribution, seeU.S. patent application Ser. No. 10/453,395, entitled: Systems, Methodsand Computer Program Products for Modeling a Monetary Measure for A GoodBased Upon Technology Maturity Levels, filed Jun. 3, 2003, the contentsof which are hereby incorporated by reference in its entirety.

Regardless of how the price sensitivity distribution is determined, inaddition to factoring uncertainty in the price of the good into thedemand for the good, the demand can advantageously be modeled as afunction of the size of the market within which the good is purchased tothereby account for uncertainty in the size of the market. In thisregard, uncertainty in the size of the market is typically representedas a market potential that refers to the total number of units of thegood consumers will purchase presuming all consumer requirements aremet, including price, as shown in block 24 of FIG. 2. The marketpotential is typically expressed as a distribution of consumerspurchasing a predetermined number of units of the good. The marketpotential distribution generally assigns a probability to eachrespective number of units of the good consumers will purchase presumingall consumer requirements are met. Like the market sensitivitydistribution, the market potential distribution can be expressed in anyof a number of different types of distributions but, in one embodiment,is expressed as a lognormal probability distribution. For moreinformation on such a market potential distribution, see U.S. patentapplication Ser. No. 10/453,727 entitled: Systems, Methods and ComputerProgram Products for Modeling Demand, Supply and AssociatedProfitability of a Good.

As stated, the demand for the good is modeled as a function of the sizeof the market within which the good is sold. Thus, to model the demandfor the good a forecasted market of a predefined total number of unitsof the good is selected from the market potential distribution.Advantageously, the number of units in the forecasted market is selectedaccording to a method for randomly selecting a predefined number ofunits of the good, such as the Monte Carlo method, as shown in block 26.And as described below, by repeatedly selecting different forecastedmarkets, a corresponding demand for the good can be modeled for eachforecasted market to thereby facilitate an understanding of howdifferent market sizes affect demand for the good.

As manufacturers will typically not be capable of capturing all (i.e.,100%) of the market for a good, demand for the good can be modeled toaccount for different percentages of the market that a manufacturer maycapture. Therefore, from the forecasted market selected, a marketpenetration distribution can be determined based upon different numbersof units that represent corresponding percentages of the forecastedmarket, as shown in block 28. For example, as shown in FIG. 4, in amarket size of 700 units of the good, a sale of 350 units would beassociated with a market penetration of 50%. Once the market penetrationdistribution has been determined, the demand can be modeled based uponthe price sensitivity distribution and the market penetrationdistribution. To combine the price sensitivity distribution and themarket penetration distribution, the price sensitivity distribution isfirst recast in reverse cumulative format, as shown in FIG. 3. (See FIG.2, block 30). As will be apparent, a reverse cumulative distributiondepicts the number, proportion or percentage of values greater than orequal to a given value. In this regard, the reverse cumulative of theprice sensitivity distribution represents the distribution of customerswilling to purchase the good for at least a predetermined price, i.e.,at or above a predetermined price.

Once the price sensitivity distribution has been recast, the demand forthe product for the forecasted market can be modeled based upon thereverse cumulative of the price sensitivity distribution and the marketpenetration distribution, as shown in block 32 of FIG. 2. In thisregard, the demand represents the number of units consumers willpurchase for at least a given price, i.e., at or above a given price. Tomodel the demand, each probability percent of the reverse cumulative ofthe price sensitivity distribution is associated with a correspondingpercentage of the forecasted market from the market penetrationdistribution. Thus, each of a plurality of different numbers of units ofthe good from the market penetration distribution are linked to aminimum price per unit from the reverse cumulative price sensitivitydistribution having a probability percent equal to the marketpenetration percent for the respective number of units. As such, thedemand model can be thought of as a plurality of different numbers ofunits sold in the forecasted market, each number of units having acorresponding minimum price at which consumers will purchase therespective number of units. For example, a number of goods totaling 700and having a market penetration of 100% is linked to a price per unit ofapproximately $77 million dollars having a probability percent of 100%.Thus, according to the demand model, 700 units of the good will be soldfor at least $77 million dollars. The demand model can be represented inany one of a number of manners but, in one embodiment, the demand modelis represented as a demand curve by plotting different numbers of unitssold in the forecasted market versus the minimum price consumers willpay per unit for the good, as shown in FIG. 5.

It will be appreciated that the demand for the good is based upon thereverse cumulative of the price sensitivity distribution and the marketpenetration distribution. Thus, the steps in determining the reversecumulative of the price sensitivity distribution and the marketpenetration distribution can be accomplished in any order relative toone another without departing from the spirit and scope of the presentinvention. For example, the price sensitivity distribution can berewritten in reverse cumulative format before any or all of the steps indetermining the market penetration distribution from the marketpotential distribution.

It will also be appreciated that for different numbers of units in theforecasted market, selected according to the Monte Carlo method,different market penetration distributions and, therefore, differentdemand models, will be determined as shown in FIG. 6. Thus, the demandmodel can account for the size of the market as affecting the demand forthe good. In this regard, by repeatedly selecting different forecastedmarkets and repeating the method, the demand for the good in eachforecasted market can be modeled. As described above and more fullybelow, the demand for the good can be modeled with the recurring costsin the forecasted market to thereby model the gross profit for the goodin the forecasted market which, in turn, can be used to determineconclusions regarding the forecasted market, such as the optimum priceper unit and the number of units sold. The conclusions can then beutilized to model the net profit for the good in the forecasted marketby determining the nonrecurring costs for the selected learning curvevalue. And by repeating the method for different forecasted markets, thegross and net profitability can be modeled for each forecasted market.The conclusions for the forecasted markets, as well as the gross and netprofitability models, can then be used, such as by the manufacturer, tofacilitate an understanding of how uncertainty in the price of the goodand number of units in the market affect demand, cost and profitabilityfor the good. With such an understanding, the manufacturer can be in abetter position to select a price at which to sell each unit of thegood, as well as a number of units of the good to produce.

B. Goods in Differentiated Markets

Just as in the case of non-differentiated markets, to most accuratelymodel the demand for the good in an uncertain market, the demand ispreferably modeled based upon a distribution of the possible prices forwhich the good may be sold, and a distribution of the possible sizes ofthe market within which the good may be sold. Goods in differentiatedmarkets differ from those in non-differentiated markets, however, inthat the prices per unit of the goods are not uniform across the market.In this regard, prices per unit of the goods can be uniform within eachof the plurality of contracts that include the units of the good thatmake up the market. Additionally, or alternatively prices per unit ofthe goods can be uniform within a given number of goods of the contract,such as a contract that includes 1-100 units of the good for $75M,101-200 units for $70M, 201-300 units for $65M, etc. Thus, to mostaccurately model the demand for a good purchased in a differentiatedmarket, consideration must also be given to the number of units of thegood in each contract. And because the number of units in each contractcan vary, the number of units per contract is preferably utilized inconjunction with the other distributions.

Referring now to FIG. 7, modeling the demand for a good in adifferentiated market generally begins the same as modeling the demandin a non-differentiated market, that is by assessing uncertainty in theprice per unit of the good by determining how the price of the goodaffects whether customers will purchase the good. In this regard, theprice sensitivity of the good is typically expressed as before with theprice sensitivity distribution, as shown in block 34. The marketpotential can likewise be expressed as before by a market potentialdistribution of consumers purchasing a predetermined number of units ofthe good, as shown in block 36. Also, as before, the demand is modeledas a function of the size of the market within which the goods are soldto thereby account for uncertainty in the size of the market. Thus, tomodel the demand for the product based on a forecasted market, thepredefined number of units of the good in the forecasted market isselected from the market potential distribution according to the MonteCarlo method, as shown in block 38. Just as in the case ofnon-differentiated markets, and as described below, by repeatedlyselecting different forecasted markets, a corresponding demand for thegood purchased in a differentiated market can be modeled for eachforecasted market.

As previously stated, non-differentiated markets differ fromdifferentiated markets in that goods in non-differentiated markets areall sold and purchased for a uniform price, as opposed to differingprices based on individual units. In a differentiated market, the goodsare sold according to contracts that each specify a predetermined numberof units of the good at a predetermined price for each unit. Thus, thereare many prices (one for each contract) for a forecasted market. Assuch, for differentiated markets, modeling the demand for the goodfurther includes assessing the uncertainty in the number of contracts inthe market, as well as uncertainty in the predetermined number of unitsof the good in each contract and the predetermined price per unit atwhich each unit in each contract is purchased. In this regard,uncertainty in the number of units in each contract can be assessed bydetermining a units per contract distribution, shown in block 40.

Like the price sensitivity and market potential distributions, the unitsper contract distribution is typically expressed as a distribution ofunits of the good included in each contract. The units per contractdistribution generally assigns a probability to each respective numberof units that may be included in a particular contract. The units percontract distribution can be expressed according to any of a number ofdifferent probability distribution types but, in one embodiment, isexpressed as a lognormal probability distribution. For more informationon such a units per contract distribution, see U.S. patent applicationSer. No. 10/453,727 entitled: Systems, Methods and Computer ProgramProducts for Modeling Demand, Supply and Associated Profitability of AGood.

With the price sensitivity distribution and the units per contractdistribution, a contract purchases collection can be determined toinclude a number of contracts, each having a number of units of the goodand an associated price per unit. Before determining the contractpurchases collection, the forecasted market can be selected, such asaccording to the Monte Carlo method, so that the total number of unitsin all of the contracts included within the contract purchasescollection can be based upon the forecasted market. Presuming a totalcapture of the forecasted market by the manufacturer (i.e., selling allof the units in the entire market), the total number of units in all ofthe contracts can then be set equal to the number of units in theforecasted market. But presuming less than a total capture of theforecasted market, the total number of units in all of the contracts canbe set equal to a percentage of the number of units in the forecastedmarket. Whereas the method of the present invention described belowrefers to the forecasted market, it should be understood that ininstances where less than a total capture of the forecasted market ispresumed, the presumed capture of the forecasted market will preferablybe utilized in place of the number of units in the forecasted market.

To determine the contract purchases collection, a relationship betweenthe price sensitivity distribution and the units per contractdistribution is first established (see FIG. 7, block 42), such as via acorrelation coefficient. The correlation coefficient can be selected inany one of a number of manners, however, the correlation coefficientshould be a non-positive number. In one embodiment, for example, thecorrelation coefficient is determined in accordance with conventionaltechniques based upon a number of historical contractual sales of thegood or a similar good, where each sale includes a number of units ofthe good at a price per unit. For more information on determining such acorrelation coefficient, see U.S. patent application Ser. No. 10/453,727entitled: Systems, Methods and Computer Program Products for ModelingDemand, Supply and Associated Profitability of A Good.

Once the price sensitivity distribution is related to the units percontract distribution, the contract purchases collection can bedetermined by first determining the number of contracts and the numberof units in each contract, as shown in block 44. The number of contractscan be determined in any of a number of different manners, such as byselecting a predefined number of contracts based upon the forecastedmarket and the number of units in each contract based upon historicalcontracts of the same or similar goods. Like the forecasted market, thenumber of units in each contract are typically determined according tothe Monte Carlo method based upon the units per contract distribution.Because the forecasted market has been defined to include a predefinednumber of units of the good in the market, the aggregate number of unitsin each contract within the forecasted market totals the predefinednumber of units in the forecasted market or, alternatively, a percentageof the predefined number of units if less than total market capture ofthe forecasted market is presumed. In this regard, the Monte Carlomethod can be used to repeatedly select different numbers of units ineach contract, so long as the aggregate number of units in each contractwithin the forecasted market does not exceed the predefined number ofunits in the forecasted market (or percentage of the predefined number).By repeatedly selecting different numbers of units in the predefinednumber of contracts in the forecasted market, many different contractpurchases collections can be determined for the forecasted market.

Either as the number of units in each contract is determined, or afterthe number of units is determined, the associated price per unit of theunits in each contract is determined (e.g., according to a Monte Carlomethod) based upon the number of units in the respective contract, theprice sensitivity distribution and the correlation between the units percontract distribution and the price sensitivity distribution, as shownin block 46. With the number of units per contract and the associatedprice per unit of the units in each contract, the contract purchasescollection can be determined as a plurality of contracts, with eachcontract having an associated number of units of the good at a givenprice per unit, as shown in block 48. The contract purchases collectioncan be represented in any one of a number of manners but, in oneembodiment, the contract purchases collection is represented as ascatter plot of the units in each contract at the corresponding priceper unit, as shown in FIG. 8 with a forecasted market of 681 units and apresumed market capture of 60% (i.e., 409 units).

As described above, the contract purchases collection can be determinedby determining a correlation between the price sensitivity distributionand the units per contract distribution, selecting a number of contractsand a number of units in each contract according to the Monte Carlomethod, and thereafter determining a price per unit contract. It will beunderstood, however, that the contract purchases collection can bedetermined in any of a number of different manners. For example, thecontract purchases collection can be determined by determining thecorrelation and thereafter selecting a number of contracts, such asrandomly selecting a defined number of contracts (e.g., 100 contracts).With the number of contracts, then, a price sensitivity distribution anda units per contract distribution can be defined for each contract,where the distributions can differ between one or more contracts orremain the same across all of the defined number of contracts. Where thedistributions differ between one or more contracts, the correlation cansimilarly differ but, when the distributions remain the same across allof the contracts, the correlation is preferably the same across all ofthe contracts. It will be understood that the values from the pricesensitivity distribution and the units per contract distributions aretypically generated according to a Monte Carlo method using thecorrelation value. As such, it will also be understood that the priceper unit for each contract can be determined before, after or as theunits per contract are determined.

For each of the defined contracts, then, a number of units in therespective contract can be determined, such as from the units percontract distribution according to the Monte Carlo method. Then, anassociated price per unit for each of the defined contracts can bedetermined based upon the number of units in the respective contract,the respective price sensitivity distribution and the correlationbetween the units per contract distribution and the price sensitivitydistribution. Thereafter, as before, with the number of units percontract and the associated price per unit of the units in eachcontract, the contract purchases collection can be determined as aplurality of contracts, with each contract having an associated numberof units of the good at a given price per unit.

As before, the demand for the good in the forecasted market representsthe number of units consumers will purchase for at least a given price.In this regard, the price per unit of each contract can be ranked indescending from the highest price per unit down. A cumulative number ofunits for each different price per unit can then be calculated, as shownin block 50 of FIG. 7. The cumulative number of units for each pricethen would equal the cumulative number units across all of the contractssold for a price per unit equal to or greater than the respective price.For example, the cumulative number of units associated with the highestprice per unit would equal the number of units in each contact havingthe highest price per unit. Then, the cumulative number of unitsassociated with the second highest price per unit would equal the numberof units in each contract having the second highest price per unit plusthe number of units in each contact having the highest price per unit.

It will be appreciated, however, that the price per unit of eachcontract can equally be ranked in ascending order from the lowest priceper unit up. In such an instance, the cumulative number of units foreach price would equal the total number of units in the forecastedmarket minus the number of units in each contract with a price per unitlower than the respective price. For example, the cumulative number ofunits associated with the lowest price per unit would equal the numberof units in the forecasted market or, alternatively, the percentage ofthe forecasted market. The cumulative number of units associated withthe second lowest price per unit would then equal the number of units inthe forecasted market minus the number of units in each contract withthe lowest price per unit.

With each different price per unit and the associated cumulative numberof units, the demand for the good in the forecasted market, orpercentage of the forecasted market, can be modeled based upon the priceper unit of each of the contracts and the cumulative number of unitssold for a price per unit equal to or greater than the respective priceper unit, as shown in block 52. In this regard, as with the demand modelfor a good in a non-differentiated market, the demand model for a goodin a differentiated market represents the number of units consumers willpurchase for at least a given price. As such, the demand model can bethought of as a plurality of different numbers of units sold in theforecasted market, each number of units having a corresponding minimumprice at which consumers will purchase the respective number of units.The demand model can be represented in any one of a number of mannersbut, like in the case of the model for the non-differentiated market, inone embodiment the demand model is represented as a demand curve byplotting the different prices per unit versus the cumulative number ofunits sold for a price per unit equal to or greater than the respectiveprice per unit, as shown in FIG. 9 with a forecasted market of 681 unitsand a presumed market capture of 409 units. As illustrated, the demandmodel will not appear as smooth as the demand in the case of thenon-differentiated market. The coarseness of the demand model for thedifferentiated market is due to the fact that the model uses distinctcontractual sales, as opposed to considering the entirenon-differentiated market as one contractual sale.

It will be appreciated that as the total number of units in theforecasted market changes according to the Monte Carlo method for thedemand model for either the case of the non-differentiated market or thedifferentiated market, the demand model changes to fit the total numberof units of the good. It will also be appreciated that for differentnumbers of units in the forecasted market, selected according to theMonte Carlo method, different values from the market penetrationdistributions and contract purchases collections will be determined forthe good in the differentiated and non-differentiated market,respectively. And with the different market penetration distributionsand different contract purchases collections, different demand modelswill be determined for each forecasted market. Thus, the respectivedemand models can account for the size of the market as affecting thedemand for the good. In this regard, by repeatedly selecting differentforecasted markets and repeating the method, the demand for the good ineach forecasted market can be modeled.

As indicated above and described more fully below, modeling the demandfor the good can be utilized with the recurring costs and nonrecurringcosts models to thereby model the gross and net profitability of thegood in the forecasted market which, in turn, can be used to determineconclusions regarding the forecasted market, such as the learning curvevalue, the optimum price per unit and the number of units sold. And byrepeating the method for different forecasted markets, the profitabilitycan be modeled for each forecasted market, and the conclusions can bedetermined for each forecasted market. The conclusions for theforecasted markets can then be used, such as by the manufacturer, tofacilitate an understanding of how uncertainty in the price of the good,the number of units and/or contracts, as well as the price per unit ofthe good in the contracts, affects demand for the good. With such anunderstanding, then, the manufacturer can be in a better position toselect a learning curve value, a price at which to sell each unit of thegood and a number of units of the good to produce.

II. Modeling Costs Associated with Producing the Good

As stated above, costs can be divided into two different types,nonrecurring and recurring. As such, each can be modeled separately, aswill be described below.

A. Modeling Recurring Costs

The recurring and nonrecurring costs can be modeled according to any ofa number of different techniques. As an example of one method by whichthe recurring costs to manufacture each unit of a good can be modeled,reference is now made to FIGS. 10-16. Modeling the recurring costs toproduce each unit of the good generally begins with assessinguncertainty in the recurring cost to produce each unit of the good,typically represented as a measure of how the cost of producing the goodaffects whether manufacturers will produce the good. In this regard, thecost sensitivity of the good is typically expressed as a distribution ofmanufacturers producing the good at a predetermined price. The costsensitivity distribution generally assigns a probability of producingone unit of the good to each respective cost at which manufacturerswould produce the good. Whereas the cost sensitivity can be expressed asany of a number of different types of distributions, the costsensitivity according to the example is expressed as a lognormalprobability distribution, and defined according to the mean and standarddeviation of cost data, such as can be determined from market studies,cost analyses or the like. For example, the cost sensitivitydistribution shown in FIG. 13 is defined according to a mean of $56,806(in millions of dollars) with an associated standard deviation.

Like the price sensitivity distribution, the cost sensitivitydistribution can be determined based upon the state of development oftechnologies associated with the good. In such instances, the costsensitivity distribution can be determined as described above inconjunction with the price sensitivity distribution. In contrast to thecost sensitivity distribution, however, a cost point, or more typicallya most likely recurring cost, is selected for each technology. Then, acost distribution can then be defined for each technology based upon thedistribution associated with the respective qualitative measure ofmaturity and the respective most likely cost. From a number of possibletotal recurring costs determined from costs selected from the respectivedistributions, a mean and standard deviation can be determined tothereby define the cost sensitivity distribution. For more informationon such a method of determining the cost sensitivity distribution, seeU.S. patent application Ser. No. 10/453,395, entitled: Systems, Methodsand Computer Program Products for Modeling a Monetary Measure for A GoodBased Upon Technology Maturity Levels.

To model recurring costs, a market is first forecast by selecting thenumber of units produced, as shown in block 54 of FIG. 10A. Thereafter,a potential learning curve value is selected from a set of potentiallearning curve values, as shown in block 56. The set of potentiallearning curve values can comprise all integers between zero and onehundred. In a more typical embodiment, however, the learning curve valueis selected from a set including all integers between 70 and 100. In theexample method, as previously stated, modeling the recurring cost toproduce each unit of the good in the forecasted market includesassessing uncertainty in the cost of producing the good, as such may berepresented as a measure of how the cost of producing the good affectswhether manufacturers will produce the good, as such is typicallyexpressed by the cost sensitivity distribution (see FIG. 13).

Modeling the recurring costs associated with the production of a good inan uncertain market is typically based on the average cost per unit toproduce the good and the number of units produced, or sold. The cost ofproducing the good can be modeled in any one of a number of manners, butpreferably considers the effect of the number of units produced, orsold, on the cost to produce each unit of the good. In this regard,costs associated with producing a good in many markets tend to declineas the manufacturer gains experience with that production. Whereas onemight expect the cost of producing each unit of the good to remainconstant, the cost to produce the first units of the good is typicallymore than the expected cost of producing subsequent units. And as thenumber of units produced increases, the manufacturer gains experiencethat drives the cost to produce each unit down to the expected cost andbelow, and thereafter eventually leveling to an optimum cost ofproducing each unit. The change in the cost to produce each unit cangenerally be considered to be attributable to learning. In this regard,a learning curve value describes the amount of learning that a processcan achieve or how much the cost declines with production.

To account for the learning curve for producing the good, modeling therecurring cost may further include using a learning curve. In thisregard, the recurring cost model may be generally defined according to anumber of characteristics, such as the learning curve type, the selectedpotential learning curve value, and calibration values, as such may bedetermined as described below. Further, the recurring cost model may befitted to the size of the forecasted market.

In one embodiment, for example, the recurring cost model can bedetermined for each forecasted market. As shown in FIG. 11, inembodiments in which the learning curve type is log-linear (i.e., has alinear shape in log-log space), an intermediate value (Learn Calc) fordetermining the recurring cost model can be calculated as follows:

${{LearnCalc} = \frac{\begin{pmatrix}{{1/({coeff\_ factor})} \times} \\\left( {\left( {{CumUnits} + 0.5} \right)^{{coeff}\_ {factor}} - \left( {1 - 0.5} \right)^{{coeff}\_ {factor}}} \right.\end{pmatrix}}{\begin{pmatrix}{{1/({coeff\_ factor})} \times} \\\left( {\left( {{CalUnits} + 0.5} \right)^{{coeff}\_ {factor}} - \left( {1 - 0.5} \right)^{{coeff}\_ {factor}}} \right.\end{pmatrix}}},$

where coeff_factor=((ln(LC/100))/ln(2))+1. In the foregoing equations,LC represents the selected potential learning curve value, CumUnitsrepresents the cumulative number of units of the good sold in theforecasted market, and CalUnits represents the number of units themanufacturer must produce to have an average cost per unit equal to theconstant expected cost of producing each unit. It will be appreciatedthat although the learning curve type has been described as being alog-linear type learning curve, the learning curve can be any of anumber of different types of learning curves, such as a Stanford-B typelearning curve, a DeJong type learning curve, an S-Type learning curveor the like.

Either before, after or as the learning curve type is determined, thecost to manufacture the first unit of the good (i.e., the T#1 cost) canbe determined. Whereas the T#1 cost can be determined in any of a numberof different manners, in one embodiment the T#1 cost is determined basedupon the selected potential learning curve value from a model of T#1cost as a function of potential learning curve values, as shown in block58, and described more fully below. As shown in block 60, afterdetermining the T#1 cost, the recurring cost can be modeled in theforecasted market for the selected potential learning curve value by thefollowing equation:

${{Recurring}\mspace{14mu} {Cost}} = {T{\# 1}\mspace{14mu} {Cost} \times \frac{CalUnits}{{Cu}\; {mUnits}} \times {LearnCalc}}$

where T#1 Cost in the above equation represents the T#1 cost determinedfrom the T#1 cost model. The recurring costs model for the forecastedmarket can be represented in any one of a number of different mannersbut, in one embodiment, the cost model is represented as an averagerecurring cost curve by plotting the average cost per unit versus thecumulative number of units produced, as shown in FIG. 12.

As stated above, in modeling recurring costs, the T#1 cost can bedetermined from a model of T#1 cost as a function of potential learningcurve values. In this regard, the T#1 cost can be modeled as a functionof potential learning curve values in any of a number of differentmanners. In one embodiment, now referring to FIG. 10B, a method ofmodeling the T#1 cost begins by selecting a unit cost from the costsensitivity distribution (see FIG. 13), as shown in block 62.Advantageously, the unit cost can be selected according to a method forrandomly selecting a predefined unit cost, such as the Monte Carlomethod. In this regard, the Monte Carlo method is applied to the costsensitivity distribution to select the predefined unit cost.

After selecting the unit cost, a fixed cost associated with producingthe first unit of the good, referred to as the fixed T#1 cost, isdetermined based upon the selected unit cost, as shown in block 64.Additionally, the fixed T#1 cost can be determined based upon a numberof benchmark characteristics, such as a benchmark learning curve value,and a benchmark calibration value associated with the number of unitsthe manufacturer must produce to have an average cost per unit equal tothe selected cost of producing each unit. The benchmark values can beselected in a number of different manners, such as from market studies,cost analyses or the like. For example, the benchmark learning curvevalue can be selected to be 85, while the benchmark calibration value isset at 500. With the selected unit cost, benchmark learning curve valueand benchmark calibration value, then, the fixed T#1 cost can bedetermined. The fixed T#1 value can be determined in any of a number ofdifferent manners but, in one embodiment, the fixed T#1 cost isdetermined as follows:

${{Fixed}{\mspace{11mu} \;}T{\# 1}} = \frac{{Unit}{\mspace{11mu} \;}{Value}}{\begin{matrix}{{Benchmark}\mspace{14mu} {Calibration}} \\{Value}^{\frac{({{\log_{10}{({{Benchmark}\mspace{14mu} {Learning}\mspace{14mu} {Curve}\mspace{14mu} {Value}})}} - 2})}{\log_{10}{(2)}}}\end{matrix}}$

For example, presuming the unit cost is selected from the costsensitivity distribution to equal $54,000, and the benchmark learningcurve value and calibration value set at 85 and 500, respectively, thefixed T#1 cost can be determined to equal $231,851.

After determining the fixed T#1 cost, the recurring cost to produce thegood can be determined in a manner that advantageously accounts for howthe recurring cost to produce the first unit, the T#1 cost, relates tothe recurring cost to produce subsequent units as a function ofdifferent, potential learning curve values. In this regard, therelationship between the recurring cost for subsequent units and the T#1cost can be represented by a variance factor which, in turn, can bedetermined as a function of potential learning curve values. Moreparticularly, the variance factor can reflect the level of recurringcosts as compared to the standard, or benchmark, fixed T#1 cost. As willbe appreciated, then, a variance factor of one is standard. The higherthe variance factor, the higher the recurring costs to the standard,fixed T#1 cost. In contrast, the lower the variance factor, the lowerthe recurring costs to the standard, fixed T#1 cost.

To determine the variance factor, variance is determined as a functionof potential learning curve values, as shown in block 66. The variancecan be determined in a number of different manners such as, for example,by establishing a number of variance values associated with differentlearning curve values. The variance values and learning curve values canbe established in a number of different manners. In one embodiment,shown in FIG. 14A, the variance values and learning curve values areestablished from theoretical T#1 variance values associated withdifferent learning curve values, as such may be determined by anestimator or the like. After establishing the variance values andassociated learning curve values, a best fit curve of variance as afactor of potential learning curve values can be established accordingto the unit curve theory based upon the data, as shown in FIG. 14B. Forexample, the best fit curve can be established as follows:

Variance(Learning Curve Value)=a+e ^(b+c×Learning Curve Value)

In the above, equation, a, b and c are constants that are selected basedupon the best fit curve which, in turn, is based upon the variancevalues and associated learning curve values. In one embodiment, forexample, the values of a, b and c are selected to be 2.61, 16.61 and−0.1836, respectively.

Although the best fit curve can be established as indicated above, itwill be appreciated that a number of different best fit curves can beestablished based upon assumptions made about the curve (e.g., thevariance decreases as the learning curve value increases, variancechanges less as the learning curve value increases, etc.). Thus, anumber of different best fit curves can be established based upon thevariance values and learning curve values, with all of the best fitcurves generally fitting the data. The best fit curve, then, can beestablished as desired, with the above best fit curve established toprovide an desired amount of control over the curve, with the values ofa, b and c being capable of being easily modified.

After determining the variance as a factor of potential learning curvevalues, the variance factor as a function of potential learning curvevalues can be determined based upon the variance and a benchmarkvariance determined based upon the benchmark learning curve value, asshown in block 68. For example, according to one embodiment, thevariance factor can be determined as follows:

${{Variance}\mspace{14mu} {Factor}\; \left( {{Learning}\mspace{14mu} {Curve}\mspace{14mu} {Value}} \right)} = \frac{\begin{matrix}{Variance} \\\left( {{Learning}\mspace{14mu} {Curve}\mspace{14mu} {Value}} \right)\end{matrix}}{\begin{matrix}{Variance} \\\begin{pmatrix}{{Benchmark}{\mspace{11mu} \;}{Learning}} \\{{Curve}\mspace{14mu} {Value}}\end{pmatrix}\end{matrix}}$

Substituting the example values of a, b, c and the benchmark learningcurve value given above, then, the variance factor can be determined tobe:

${{Variance}\mspace{14mu} {Factor}\; \left( {{Learning}\mspace{14mu} {Curve}\mspace{14mu} {Value}} \right)} = \frac{\begin{matrix}{2.61 +} \\^{16.61 - {{.1836} \times {Learning}\mspace{14mu} {Curve}\mspace{14mu} {Value}}}\end{matrix}}{5.34}$

After determining the variance factor, the T#1 cost associated withproducing the good can be modeled as a function of potential learningcurve values based upon the variance factor and the fixed T#1 cost, asshown in block 70. In one embodiment, for example, the T#1 cost can bemodeled by multiplying the variance factor by the fixed T#1 cost. Inmathematical terms, then, the T#1 cost can be modeled as a factor ofpotential learning curve values as follows:

T#1(Learning Curve Value)=Variance Factor(Learning Curve Value)×FixedT#1

After modeling the T#1 cost as a function of potential learning curvevalues, recurring costs can be modeled as a function of potentiallearning curve values. As will be appreciated, each learning curve mayhave many possible values of recurring cost. As such, in one moreparticular embodiment, the recurring costs that optimize net profits,taking into account demand for the good in a forecasted market, can bemodeled as a function of potential learning curve values, as shown inFIG. 15. It will be appreciate that, as shown, the recurring costs dropdramatically when the learning curve value exceeds a certain value(approximately 93 as shown in FIG. 15). In this regard, in the contextof producing a good, the drop in recurring costs at high learning curvevalues typically corresponds to instances in which a manufacturer wouldnever recoup the non-recurring costs associated with a good to turn aprofit. Thus, the manufacturer would typically not produce the good whenthe non-recurring costs and, thus, learning curve value, exceed acertain value. Although not shown in FIG. 15, the recurring costs alsodecrease dramatically when the learning curve value drops below acertain value. In the context of producing a good, the drop in recurringcosts at low learning curve values can correspond to instances in whichthe improvement in producing the good over time and, thus, drop inrecurring costs over time, would be very small. In such instances, itwould require such an undesirable amount of time for the recurring coststo reach a point where the manufacturer would turn a profit, if therecurring costs ever reached such a point, that the manufacturer wouldlikely elect to not produce the good.

Just as in the case of modeling demand for the good, the recurring costto produce the good differs between non-differentiated anddifferentiated markets. The recurring costs of producing the good in thedifferentiated market can be modeled in any one of a number of manners,such as according to the method described above in conjunction withselecting a learning curve value and modeling the recurring costs in theforecasted market in the case of non-differentiated goods. Because thedemand for the good in the forecasted market represents the number ofunits consumers will purchase for at least a given price, the learningcurve used to model the recurring costs are based upon the selectedlearning curve value and is a function of the cumulative number of unitsassociated with each price per unit, as described above in conjunctionwith modeling the demand for goods in a differentiated market. As shownin FIG. 16, just as the demand for the differentiated market appearscoarse as a plurality of connected contractual sales, the recurringcosts curve likewise appears as a plurality of connected costs forproducing respective cumulative numbers of units for each price perunit.

B. Modeling Nonrecurring Costs

Reference is now drawn to FIGS. 17A and 17B, which illustrate twoembodiments of a method of modeling the nonrecurring costs associatedwith producing a good. To model the nonrecurring costs according to theillustrated embodiment of FIG. 17A, the nonrecurring costs are firstrelated to potential learning curve values, as shown in block 72. Thenonrecurring costs can be related to potential learning curve values ina number of different manners such as, for example, by establishing anumber of nonrecurring costs values associated with different learningcurve values. The nonrecurring costs values and learning curve valuescan be established in a number of different manners and, in oneembodiment shown in FIG. 18A, the nonrecurring costs values and learningcurve values are established from theoretical nonrecurring costs valuesassociated with different learning curve values, as such may bedetermined by an estimator or the like.

After establishing the nonrecurring costs values and associated learningcurve values, then, a best fit curve of nonrecurring costs as a factorof potential learning curve values can be determined according to theunit curve theory based upon the data, as shown in FIG. 18B. Forexample, the best fit curve of nonrecurring costs can be established tobe:

Nonrecurring Cost(Learning Curve Value)=d×e ^(f+g×Learning Curve Value)

In the above, equation, constants d and g are constants that are basedupon the best fit curve, and can be selected in a number of differentmanners, as shown in block 74. In this regard, d can be considered ascale factor that allows the nonrecurring costs value to be scaled toany number of different cost levels. For example, in one embodiment thenonrecurring costs assumes that cost levels are 10⁶ (i.e., d=10⁶) timesgreater than the determined value such that cost values determined arescaled by a million dollars. The constant g can be considered a learningcurve value sensitivity value that measures how much the learning curvevalue affects the nonrecurring costs. As such, g can be selected asdesired. In one embodiment, for example, g can be selected to equal−0.257.

The constant f can be considered a measure of uncertainty, referred toherein as an uncertainty value, that directly affects the nonrecurringcosts value. And as the uncertainty of the nonrecurring costs value cantypically vary, the constant is preferably selected from a distribution,such as a risk distribution, as shown in block 76. The risk distributioncan be determined in any of a number of different manners, such as by anestimator or the like. Similarly, the risk distribution can berepresented by any of a number of different distributions but, in oneexample, the risk distribution is represented by a triangulardistribution, as shown in FIG. 19. As shown in FIG. 19, for example, therisk distribution can be represented by a triangular distribution havinga minimum value of −8.20, a maximum value of −7.80, and a mode of −8.00.Like the cost sensitivity distribution, the uncertainty value f canadvantageously be selected according to a method for randomly selectinga predefined unit cost, such as the Monte Carlo method. For example,from the risk distribution shown, the uncertainty value can be selectedto equal −8.12.

As before, it will be appreciated that a number of different best fitcurves can be established based upon assumptions made about the curve(e.g., the nonrecurring costs increase as the learning curve valueincreases, nonrecurring costs change less as the learning curve valuedecreases, etc.). Thus, a number of different best fit curves can beestablished based upon the nonrecurring costs values and learning curvevalues, with all of the best fit curves generally fitting the data. Thebest fit curve, then, can be established as desired, with the above bestfit curve established to provide an desired amount of control over thecurve, with the values of d, f and g being capable of being easilymodified.

After selecting the constants d, f and g, the nonrecurring costs toproduce the good can be modeled as a function of potential learningcurve values, as shown in block 78. For example, according to oneembodiment, the nonrecurring costs can be modeled by substituting thevalues for d, f and g into the best fit curve for nonrecurring costs.According to the examples given above for d, f and g, in mathematicalterms the nonrecurring costs (NRC) can be modeled as a factor ofpotential learning curve values as follows:

NRC(Learning Curve Value)=10⁶ ×e ^(−8.12 −0.257×Learning Curve Value)

Like the recurring costs model, the nonrecurring costs model can berepresented in any one of a number of manners but, in one embodiment,the nonrecurring costs model is represented as a recurring costs curveby plotting the nonrecurring costs over a range of potential learningcurve values, as shown in FIG. 20.

Similar to the price sensitivity distribution and the cost sensitivitydistribution, uncertainty in the nonrecurring cost of the good can bedefined based upon a state of development of technologies associatedwith the good. Referring now to FIG. 17B, another embodiment of modelingnonrecurring costs can account for the state of development of thetechnologies associated with the manufacture of the good. In thisembodiment, nonrecurring costs are modeled by first associating eachtechnology associated with the nonrecurring costs to produce the goodwith a qualitative measure of maturity, where each qualitative measureof maturity is associated with a distribution, as shown in block 80. Assuch, each nonrecurring technology is associated with the distributionof the respective qualitative measure of maturity. In this regard, eachnonrecurring technology can be associated with high and low nonrecurringcost values based upon the respective distribution, as shown in block82. As described more fully below, such high and low nonrecurring costvalues for the respective distributions can then be used to determine arisk distribution for the respective nonrecurring technologies.

After associating each nonrecurring technology with the distribution ofthe respective qualitative measure of maturity, a cost point, or moretypically a most likely nonrecurring cost (MLC), is selected for eachtechnology, such as by the user. To determine the mode of the riskdistribution for each nonrecurring technology, the equation for the bestfit curve for nonrecurring costs can be rewritten to solve for theuncertainty value f as follows:

$f = {{\ln \left( \frac{MLC}{d} \right)} - {g \times {LearningCurveValue}}}$

In the above equation, f represents the mode of the risk distributionfor the respective nonrecurring technology, MLC represents the mostlikely nonrecurring cost, and d and g represent the scale factor andlearning curve value sensitivity value, respectively. Also in the aboveequation, Learning Curve Value represents the benchmark learning curvevalue, as such is described above with respect to modeling T#1 cost.

With the high and low nonrecurring cost values and the mode for eachnonrecurring technology, a risk distribution can be defined for eachnonrecurring technology. Thereafter, as shown in block 86, anuncertainty value (f as described above in conjunction with FIG. 17A)can be selected for each nonrecurring technology, such as according tothe Monte Carlo method.

As will be appreciated, in some instances it may be desirable to holdconstant the learning curve value for one or more nonrecurringtechnologies, such as when examining the effect of different learningcurve values on one or more other nonrecurring technologies. As such,after selecting an uncertainty value for each nonrecurring technology,the nonrecurring technologies can be separated into those technologiesthat have variable learning curve values and those technologies thathave constant learning curve values, as shown in block 88.

For each nonrecurring technology having a variable learning curve value,nonrecurring costs are modeled as a function of potential learning curvevalues, such as by using the equation for the best-fit curve fornonrecurring costs described above, as shown in block 90. After modelingthe nonrecurring costs for such nonrecurring technologies, thenonrecurring cost models for all such nonrecurring technologies aresummed together, as shown in block 92. For each nonrecurring technologyhaving a constant learning curve value, the nonrecurring cost for therespective technologies at the respective constant learning curve valuesis determined, such as by using the equation for the best-fit curve fornonrecurring costs, as illustrated in block 94. Thereafter, thenonrecurring costs for each such nonrecurring technology are summedtogether, as shown in block 96. To model the nonrecurring costs for thegood over all of the nonrecurring technologies, then, the sum of thenonrecurring cost models for variable learning curve values is summedwith the sum of nonrecurring cost values determined for nonrecurringtechnologies with constant learning curve values, as shown in block 98.

As will be appreciated, as nonrecurring costs are typically thoseassociated with an initial investment to begin producing a good, suchcosts are typically not based upon the number of units produced, orsold. In other terms, nonrecurring costs are typically not dependentupon whether the goods are within a non-differentiated or differentiatedmarket. Therefore, the model of nonrecurring costs as a function ofpotential learning curve values will be the same for bothnon-differentiated and differentiated markets.

As will also be appreciated by those skilled in the art, modeling therecurring and nonrecurring costs are independent of one another. In thisregard, the learning curve can be determined irrespective of whether therecurring costs are modeled before or after nonrecurring costs. Thus,although recurring costs are shown and described as being modeled beforenonrecurring costs, nonrecurring costs can be modeled before modelingrecurring costs without departing from the spirit and scope of thepresent invention.

It will also be appreciated that for different unit costs selected fromthe price sensitivity distribution, selected according to the MonteCarlo method, different recurring costs models, can be determined.Similarly, for different uncertainty values selected from the riskdistribution, different nonrecurring costs models can be determined.Thus, the recurring costs and nonrecurring costs models can account forthe unit price and magnitude factor as affecting the respective costsfor the good. In this regard, by repeatedly selecting different unitcosts and/or different uncertainty values and repeating the method, therespective costs of producing the good can be modeled.

Further, it will be appreciated that the system, method and computerprogram product of embodiments of the present invention can be utilizedby manipulating data within any one of a number of commerciallyavailable computer software programs. For example, the method can beutilized by manipulating data within Excel, a spreadsheet softwareprogram distributed by the Microsoft Corporation of Redmond, Washington,including Crystal Ball, a Monte Carlo simulation software programdistributed by Decisioneering, Inc. of Denver, Colo.

III. Modeling the Profitability of a Good

By utilizing the recurring cost model, the nonrecurring cost model, andthe demand model, the profitability of the good can be modeled therebyfacilitating an understanding of how uncertainty in demand for the good,as well as uncertainty in cost of producing the good, can affectprofitability. In this regard, just as the demand model differsdepending on whether the goods are in a non-differentiated market or adifferentiated market, the profitability of the good also differsdepending on the type of market. As such, the present invention providessystems, methods and computer program products for modeling theprofitability of a good for goods in both non-differentiated markets aswell as differentiated markets.

A. Goods in Non-Differentiated Markets

Modeling the gross and net profitability, respectively, of a good in anon-differentiated market generally begins by modeling the demand forthe good according to embodiments of the present invention, as describedabove. Along with modeling the demand for the good, the recurring costsof producing the good is also modeled in the forecasted market, as alsodescribed above. Thereafter, the gross profitability of the good for theforecasted market can be modeled. In this regard, the grossprofitability can be represented as the result of subtracting the costper unit from the price per unit and multiplying the difference by thenumber of units sold for the corresponding fraction of the forecastedmarket. Thus, as shown in FIG. 21, by simultaneously plotting the demandcurve and the cost curve for the forecasted market, the grossprofitability can be seen as directly related to the distance betweenthe two curves. Like the demand model and the cost model, the grossprofitability model can be represented in any one of a number ofdifferent manners. In one embodiment, shown in FIG. 22, the grossprofitability model can be represented as a gross profitability curve byplotting the number of units that must be sold to achieve at least agiven gross profit.

From the gross profitability model, as well as the demand and recurringcosts models, conclusions regarding the forecasted market can be drawnfrom collectively modeling the demand, recurring costs and grossprofitability for the forecasted market. For example, the maximum grossprofit for the good in the forecasted market can be seen as the pointwhere the price exceeds the cost by the greatest amount. By determiningthe maximum gross profit, the optimum price per unit of the good and theoptimum number of units sold in the forecasted market (i.e., fraction ofthe number of goods in the market), as well as the correspondingrecurring costs can be determined.

After modeling the gross profitability and/or determining the maximumgross profit, the net profitability can be modeled and/or the maximumnet profit can be determined based upon the gross profitability modeland the nonrecurring costs associated with the selected learning curve.As the nonrecurring costs are not associated with the number of goodssold, as such is forecasted, the nonrecurring costs can be determined atany point after selecting the learning curve value. In this regard, thenonrecurring costs can be determined, such as is described above,utilizing the selected learning curve value.

After determining the nonrecurring costs, the net profitability of thegood can be modeled by subtracting the nonrecurring costs from the grossprofit at each point in the gross profitability model. Thus, the netprofitability model, when plotted, will appear similar to the grossprofitability model except that the net profitability model will havelower profit at each point, when compared to the gross profitability.For a comparison of the net profitability model and the grossprofitability model, see FIG. 22, where the net profitability model canbe represented as the dashed line. As will be appreciated, because thenonrecurring costs are not determined as a function of the number ofgoods sold, the maximum net profit can be determined, for example, bysimply subtracting the nonrecurring costs from the maximum gross profit.Once all potential learning curve values have been selected such thatthe maximum gross and/or net profit has been determined for each, thegross profitability and/or net profitability of the good can be modeledas a function of potential learning curve values. To model the grossprofitability as a function of potential learning curves, according toone embodiment of the present invention, the maximum gross profitabilityfor each potential learning curve value is plotted against therespective learning curve value, as shown in FIG. 23. Similar tomodeling gross profitability as a function of potential learning curvevalues, net profitability can also be modeled as a function of potentiallearning curve values. As previously indicated, net profit can bedetermined by subtracting nonrecurring costs from gross profit. In thisregard, net profitability can be modeled based upon the model of grossprofitability as a function of potential learning curves, and furtherbased upon the model of nonrecurring costs as a function of potentiallearning curve values, as such can be determined as described above. Forexample, as shown in FIG. 24, the model of net profitability as afunction of potential learning curve values can be represented as a netprofitability curve by plotting the learning curve value that must beutilized to achieve at least a given net profit. As shown, the netprofitability model illustrated has a maximum net profit when thelearning curve value is selected to equal 78, as shown by a maximum inthe net profitability curve.

At this point it should be made clear that the demand and the costmodels as functions of a forecasted market, as well as the profitabilitymodels as functions of a forecasted market, up to this point have allbeen tied to one forecasted market of a predefined number of goodsselected according to a method for randomly selecting a predefinednumber of units of the good, such as the Monte Carlo method. Further, asstated above, the recurring costs and nonrecurring costs models asfunctions of learning curve values have been tied to one unit cost anduncertainty value, respectively, selected according to any of a numberof different methods, such as the Monte Carlo method. Thus, the learningcurve value has been determined based upon a respective unit cost anduncertainty value. As such, after analyzing the forecasted market bydetermining, for example, the optimum price for each unit, optimumnumber of goods and corresponding price for each unit, as well as themaximum gross and/or net profit of the good, the conclusions can berecorded, and thereafter the method can then be repeated a plurality oftimes for different forecasted markets, as well as for different unitcosts and/or different uncertainty values to thereby determine differentlearning curve values, with the forecasted markets, unit costs and/oruncertainty values selected such as according to the Monte Carlo method,with the conclusions recorded for each forecasted market.

The conclusions for all of the forecasted markets can be organized inany of a number of different manners. For example, referring to FIG.25A, the maximum net profit for a number of different learning curvevalues can be plotted against associated learning curve values. In suchan instance, the forecasted market can be held constant based on oneselected forecasted market. Different learning curve values can then bedetermined, such as by selecting different unit costs and/or differentuncertainty values. From the different learning curve values, differentoptimum prices and different optimum numbers of units can be determined,which can thereafter be utilized to determine different maximum netprofits. In one embodiment, the maximum net profits for the differentpotential learning curve values can be averaged to produce a meanmaximum profit for the respective potential learning curve values. Themean maximum profits can then be plotted against the respective learningcurve values, as shown in FIG. 25B.

The conclusions for all of the forecasted markets can also be organizedinto respective distributions. The distributions can then be defined,such as by a curve type and a mean and associated standard deviation.From the distributions, then, a business case for the good can becreated. For example, the business case can receive distributions forthe optimum price for each unit, optimum number of goods andcorresponding price for each unit. Based upon the distributions, then,the market value of the project can be determined and plotted over time,as shown in FIG. 26. As shown, the business case can plot thenonrecurring costs associated with the project (shown below zero foryears three through five). Additionally, the business case can plot thenet profit associated with the project, as determined by the differencebetween gross profits and recurring costs (shown above zero for yearssix through fourteen).

B. Goods in Differentiated Markets

In differentiated markets, modeling the gross and net profitability alsogenerally begins by modeling the demand for a number of contracts forthe good including the number of units and associated price per unit. Inthis regard, the demand for the good can be modeled according to thepresent invention as described above with reference to FIGS. 7, 8 and 9.Similarly, the recurring cost for the good can be modeled according tothe present invention as described above with reference to FIG. 16. Inthe differentiated market, the gross profitability and net profitabilitycan therefore be represented in a manner similar to thenon-differentiated market. For example, the gross profitability can berepresented for each contract as the difference of the respective priceper unit and the respective recurring costs per unit multiplied by thenumber of units sold for the respective contract.

As will be apparent, since the demand model for the good in the contextof a differentiated market describes individual contractual sales, andthe recurring costs model describes average cost and is based on anumber of units sold, a number of units sold must be selected in orderto model the gross profitability, and thus the net profitability, of thegood for the forecasted market. If the number of contracts or the numberof units in one or more contracts changes, or if the number of units inthe presumed percentage capture of the market changes, the averagerecurring costs of producing the units for each contract would likewisechange, thus changing the model of the gross profitability and the netprofitability.

To model the gross profitability or net profitability for allpossibilities of the number of units in each contract would take anunnecessarily long period of time. But modeling the gross or netprofitability for all possibilities is not necessary. In this regard, ina differentiated market it has been found that selling and, thusproducing, as many units as possible always attains the most profit.Therefore, in modeling the profitability, the recurring costs model canbe replaced with the lowest recurring costs value for the respectiveforecasted market (shown by the dashed line on FIG. 16), or for thepercent capture of the forecasted market. The recurring costs model canbe so replaced since the lowest cost value always corresponds tocapturing the expected market share of the forecasted market and, thus,selling all of the units of the good the manufacturer produces.Profitability (gross and net), then, can be measured by theprofitability of the forecasted market (presuming total market capture)based upon the profitability of each contractual sale within theforecasted market.

Thus, from the demand model, the gross profitability of each contractualsale can be determined by subtracting the lowest average cost to producethe number of units in the contract from the price per unit of the unitsin the contract, and multiplying the difference by the number of unitsin the contract. The gross profitability of the forecasted market canthen be modeled by determining the summation of the gross profitabilityof each contractual sale.

In differentiated markets conclusions regarding the forecasted marketcan be drawn from collectively modeling the demand, cost (or lowest costvalue) and profitability for the forecasted market. For example, becausethe maximum gross profit corresponds to selling as many units aspossible, the maximum gross profit for the good in the forecasted market(or in the percent capture of the forecasted market) can be seen as thepoint where all of the units of the good in either the market, orpercent capture of the market, have been sold. Also, for example, anoptimum price to achieve maximum gross profits can be determined, suchas by determining a weighted average price per unit from all of thecontractual sales in the forecasted market (or captured percentage).Other conclusions might include the number of units in the forecastedmarket, the number of units sold in the presumed capture of theforecasted market (if less than total capture), the number of units notsold by the manufacturer in the forecasted market (again presuming lessthan total capture), and the maximum gross profit margin for theforecasted market (or captured percentage).

After modeling the gross profitability and/or determining the maximumgross profit, the net profitability can be modeled and/or the maximumnet profit can be determined based upon the gross profitability modeland the nonrecurring costs associated with the selected learning curve.As the nonrecurring costs are not associated with the number of goodssold, as such is forecasted, the nonrecurring costs can be determined atany point after selecting the learning curve value. In this regard, thenonrecurring costs can be determined, such as is described above,utilizing the selected learning curve value.

After determining the nonrecurring costs, the net profitability of thegood can be modeled by subtracting the nonrecurring costs from the grossprofit at each point in the gross profitability model. Thus, the netprofitability model, when plotted, will appear similar to the grossprofitability model except that the net profitability model will havelower profit at each point, when compared to the gross profitability. Aswill be appreciated, because the nonrecurring costs are not determinedas a function of the number of goods sold, the maximum net profit can bedetermined, for example, by simply subtracting the nonrecurring costsfrom the maximum gross profit.

It will also be appreciated that the costs associated with producing thegood, i.e., the recurring costs and the nonrecurring costs, can bemodeled as a function of potential learning curve values. The grossprofitability and/or net profitability of the good in the differentiatedmarket can also be modeled as a function of potential learning curvevalues.

To model the gross profitability as a function of potential learningcurves, according to one embodiment of the present invention, the grossprofitability is modeled based upon the contractual revenue, which canbe determined by summing the revenue generated from each contractcaptured from a given market. In addition, the gross profitability ismodeled based upon the optimum number of units (i.e., selected number ofunits) sold in the forecasted market (i.e., fraction of the number ofgoods in the market), as such may be determined as described above withrespect to the differentiated market. Further, the gross profitability,according to one embodiment, is modeled based upon the recurring costsmodel, as such may be determined as described above.

Similar to modeling net profitability as a function of potentiallearning curve values for a good in the non-differentiated market, netprofitability can also be modeled as a function of potential learningcurve values for a good in the differentiated market. As previouslyindicated, net profit can be determined by subtracting nonrecurringcosts from gross profit. As before, net profitability can be modeledbased upon the model of gross profitability as a function of potentiallearning curves, and further based upon the model of nonrecurring costsas a function of potential learning curve values, as such can bedetermined as described above in conjunction with a good in thenon-differentiated market. Also, like the model of gross profitabilityas a function of potential learning curve values, the model of netprofitability as a function of potential learning curve values can berepresented in any one of a number of different manners, such as byplotting the learning curve value that must be utilized to achieve atleast a given net profit.

Also just as in the case of non-differentiated markets, the demand andthe recurring costs, as well as the profitability of the good fordifferentiated markets, up to this point have all been tied to aforecasted market of a predefined number of goods selected according tothe Monte Carlo method. After analyzing the forecasted market bydetermining, for example, the maximum profit, the weighted averageprice, number of units and cost, the conclusions can be recorded. Oncethe conclusions have been recorded, the method can then be repeated aplurality of times for different forecasted markets selected accordingto the Monte Carlo method, with the conclusions recorded for eachforecasted market. The conclusions for all of the forecasted markets canthen be organized into respective distributions. The distributions canthen be defined, such as by a curve type and a mean and associatedstandard deviation. And from the distributions, a business case for thegood can be created, such as in a manner similar to that shown in FIG.26.

IV. Contingent Claims and Implementing Embodiments of the PresentInvention

As shown in FIGS. 25A and 25B, for certain quantities of units sold, theprofitability model actually demonstrates a negative profitability, or aloss for sales of the good. Thus, it is oftentimes desirable todetermine whether the profitability of the good is positive beforeexercising a contingent claim, such as whether to initiate or continuethe project. Alternatively, it is desirable to determine whether theprofitability of the good is above a predetermined threshold beforeexercising the contingent claim. Contingent claims oftentimes come inthe form of a call in which the manufacturer has an option to invest anamount of money, or additional amounts of money, in order to startproducing or continue producing the good. As such, if the initial stagesof the production and sale of the good have proved unsuccessful and/orif the future prospects for the profitability of the good appear bleak,the manufacturer will likely decline to invest the money, or additionalmoney, and thereby forego exercise of the call and will thereforedecline to produce the good or terminate production of the good.Alternatively, if the initial stages of the production and sale of thegood have been successful and/or if the prospects of the profitabilityof the good are bright, the manufacturer will likely make the necessaryinvestment in order to begin or continue production of the good.

Regardless of the type of contingent claim, it is desirable to determinethe value of a good and, in particular, the contingent claim at thepresent time. By determining the value of the contingent claim, themanufacturer can avoid overpaying for production of the good as a resultof an overvaluation of the contingent claim. Conversely, themanufacturer can identify goods in which the value of the contingentclaim has been undervalued and can give strong consideration toinvesting in the production of these goods since they likely representworthwhile investment opportunities. As such, by modeling the demand andcost of a good and, thus, the profitability of a good, the systems,methods and computer program products of the present invention canfacilitate determining the value of the good and, in particular, thecontingent claim at the present time. For more information ondetermining the value of the project, see U.S. patent application Ser.No. 09/902,021 entitled: Systems, Methods and Computer Program Productsfor Performing a Generalized Contingent Claim Valuation, the contents ofwhich are hereby incorporated by reference in its entirety.

Embodiments of the present invention are therefore capable of modelingthe demand and associated gross and net profitability while betteraccounting for variability in the relationship of the price of the goodand the number of units of the good purchased, as well as thevariability in the relationship of the cost of producing the good and anassociated learning curve value. As such, embodiments of the presentinvention can better model the gross and net profitability to therebymaximize such profitability.

As shown in FIG. 27, the system of the present invention is typicallyembodied by a processing element and an associated memory device, bothof which are commonly comprised by a computer 100 or the like. In thisregard, as indicated above, the method of embodiments of the presentinvention can be performed by the processing element manipulating datastored by the memory device with any one of a number of commerciallyavailable computer software programs. In one embodiment, the method canbe performed with data that is capable of being manipulated and/orpresented in spreadsheet form. For example, the method can be performedby the processing element manipulating data stored by the memory devicewith Excel, a spreadsheet software program, including Crystal Ball, aMonte Carlo simulation software program. The computer can include adisplay 102 for presenting information relative to performingembodiments of the method of the present invention, including thevarious distributions, models and/or conclusions as determined accordingto embodiments of the present invention. To plot information relative toperforming embodiments of the method of the present invention, thecomputer can further include a printer 104.

Also, the computer 100 can include a means for locally or remotelytransferring the information relative to performing embodiments of themethod of the present invention. For example, the computer can include afacsimile machine 106 for transmitting information to other facsimilemachines, computers or the like. Additionally, or alternatively, thecomputer can include a modem 108 to transfer information to othercomputers or the like. Further, the computer can include an interface(not shown) to a network, such as a local area network (LAN), and/or awide area network (WAN). For example, the computer can include anEthernet Personal Computer Memory Card International Association(PCMCIA) card configured to transmit and receive information to and froma LAN, WAN or the like.

In one advantageous technique applicable to embodiments of the presentinvention, the methods according to embodiments of the present inventionmay be embodied in a software or data module, component, portfolio orthe like, that can be manipulated or otherwise operated within aspreadsheet software program such as Excel. Such a technique may beadvantageous in a number of different contexts, such as in the contextof financial modeling and analysis. In this regard, modules, componentsand/or portfolio that perform various financial modeling functions canbe combined to gain a more complete understanding of a financialcontext. A brief description of such a technique as such may be appliedto the present invention will now be described below.

According to such a technique, data capable of being manipulated toperform at least a portion of the methods of the present invention canbe embodied in a module, which can thereafter be linked or otherwiseassociated with other portions of the methods of the present inventionembodied in other modules so as to formulate a component. Then, if sodesired, the component can be linked or otherwise associated with othercomponents capable of performing other related methods to thereby form aportfolio. For example, methods of modeling recurring and nonrecurringcosts according to embodiments of the present invention can be embodiedin one module while methods of modeling demand according to embodimentsof the present invention can be embodied in another module. The twomodules can then be linked or otherwise associated with one another toformulate a component capable of modeling profitability based upon thecost and demand models. Then, if so desired, the component for modelingprofitability can be linked or otherwise associated with anothercomponent to perform another function. For example, the component formodeling profitability can be linked or otherwise associated with acomponent capable of forecasting revenue over time to thereby create abusiness case for the good. In this regard, such a component capable offorecasting revenue over time may operate according to U.S. patentapplication Ser. No. 10/453,396, entitled: Systems, Methods and ComputerProgram Products for Modeling Uncertain Future Benefits, filed Jun. 3,2003, the contents of which are hereby incorporated by reference in itsentirety.

According to one aspect of the present invention, the system of thepresent invention generally operates under control of a computer programproduct. The computer program product for performing the methods ofembodiments of the present invention includes a computer-readablestorage medium, such as the non-volatile storage medium, andcomputer-readable program code portions, such as a series of computerinstructions, embodied in the computer-readable storage medium.

In this regard, FIGS. 1, 2, 7, 10A, 10B, 17A and 17B are flowcharts ofmethods, systems and program products according to the invention. Itwill be understood that each block or step of the flowchart, andcombinations of blocks in the flowchart, can be implemented by computerprogram instructions. These computer program instructions may be loadedonto a computer or other programmable apparatus to produce a machine,such that the instructions which execute on the computer or otherprogrammable apparatus create means for implementing the functionsspecified in the flowchart block(s) or step(s). These computer programinstructions may also be stored in a computer-readable memory that candirect a computer or other programmable apparatus to function in aparticular manner, such that the instructions stored in thecomputer-readable memory produce an article of manufacture includinginstruction means which implement the function specified in theflowchart block(s) or step(s). The computer program instructions mayalso be loaded onto a computer or other programmable apparatus to causea series of operational steps to be performed on the computer or otherprogrammable apparatus to produce a computer implemented process suchthat the instructions which execute on the computer or otherprogrammable apparatus provide steps for implementing the functionsspecified in the flowchart block(s) or step(s).

Accordingly, blocks or steps of the flowchart support combinations ofmeans for performing the specified functions, combinations of steps forperforming the specified functions and program instruction means forperforming the specified functions. It will also be understood that eachblock or step of the flowchart, and combinations of blocks or steps inthe flowchart, can be implemented by special purpose hardware-basedcomputer systems which perform the specified functions or steps, orcombinations of special purpose hardware and computer instructions.

Many modifications and other embodiments of the invention will come tomind to one skilled in the art to which this invention pertains havingthe benefit of the teachings presented in the foregoing descriptions andthe associated drawings. Therefore, it is to be understood that theinvention is not to be limited to the specific embodiments disclosed andthat modifications and other embodiments are intended to be includedwithin the scope of the appended claims. Although specific terms areemployed herein, they are used in a generic and descriptive sense onlyand not for purposes of limitation.

1. A method performed by execution of computer-readable program code byat least one processor of at least one computer system, the methodcomprising: determining, using at least one of the processors, arelationship between nonrecurring costs and potential learning curvevalues; selecting, using at least one of the processors, an uncertaintyvalue from a risk probability distribution associated with nonrecurringcosts; and generating, using at least one of the processors, a model ofnonrecurring costs to produce a good based upon the relationship betweennonrecurring costs and potential learning curve values, and theuncertainty value.
 2. A method according to claim 1, wherein determininga relationship between nonrecurring costs and potential learning curvevalues includes establishing a plurality of nonrecurring costs valuesassociated with different learning curve values, and fitting a curve todefine the relationship between nonrecurring costs values and potentiallearning curve values.
 3. A method according to claim 1, whereinselecting an uncertainty value comprises repeatedly selecting differentuncertainty values, and wherein generating a model of nonrecurring costscomprises generating a model of nonrecurring costs for each selecteduncertainty value.
 4. A method according to claim 1 further comprisinggenerating a model of profitability of the good based upon thenonrecurring costs model, recurring costs model and a demand model.
 5. Amethod according to claim 4 further comprising forecasting a marketincluding randomly selecting a predefined number of units of a goodbased upon a market potential probability distribution, whereingenerating a model of profitability comprises generating a model ofprofitability further based upon the forecasted market.
 6. A methodaccording to claim 5, wherein forecasting a market comprises repeatedlyforecasting different markets, and wherein generating a model ofprofitability comprises generating a model of profitability for each ofthe forecasted markets.
 7. A method according to claim 6, whereingenerating a model of profitability comprises generating a model ofprofitability for a plurality of potential learning curve values foreach forecasted market.
 8. A method according to claim 7 furthercomprising determining a learning curve value, wherein determining alearning curve value comprises: identifying a learning curve value foreach forecasted market such that the profitability is maximized over thepotential learning curve values; and determining a learning curve valuesuch that the mean profitability at each identified learning curve valueis maximized over the identified learning curve values.
 9. An apparatuscomprising: a processor configured to determine a relationship betweennonrecurring costs and potential learning curve values, wherein theprocessor is also configured to select an uncertainty value from a riskprobability distribution associated with nonrecurring costs, and whereinthe processor is additionally configured to generate a model ofnonrecurring costs to produce a good based upon the relationship betweennonrecurring costs and potential learning curve values, and theuncertainty value.
 10. An apparatus according to claim 9, wherein theprocessor being configured to determine a relationship betweennonrecurring costs and potential learning curve values includes beingconfigured to establish a plurality of nonrecurring costs valuesassociated with different learning curve values, and fit a curve todefine the relationship between nonrecurring costs values and potentiallearning curve values.
 11. An apparatus according to claim 9, whereinthe processor being configured to select an uncertainty value includesbeing configured to repeatedly select different uncertainty values, andwherein the processor being configured to generate a model ofnonrecurring costs includes being configured to generate a model ofnonrecurring costs for each selected uncertainty value.
 12. An apparatusaccording to claim 9, wherein the processor is further configured togenerate a model of profitability of the good based upon thenonrecurring costs model, recurring costs model and a demand model. 13.An apparatus according to claim 14, wherein the processor is alsoconfigured to forecast a market including being configured to randomlyselect a predefined number of units of a good based upon a marketpotential probability distribution, and wherein the processor isconfigured to generate the model of profitability further based upon theforecasted market.
 14. An apparatus according to claim 15, wherein theprocessor being configured to forecast a market includes beingconfigured to repeatedly forecast different markets, and wherein theprocessor being configured to generate a model of profitability includesbeing configured to generate a model of profitability for each of theforecasted markets.
 15. An apparatus according to claim 14, wherein theprocessor is configured to generate a model of profitability for aplurality of potential learning curve values for each forecasted market.16. An apparatus according to claim 15, wherein the processor is furtherconfigured to determine a learning curve value including beingconfigured to identify a learning curve value for each forecasted marketsuch that the profitability is maximized over the potential learningcurve values, and determine a learning curve value such that the meanprofitability at each identified learning curve value is maximized overthe identified learning curve values.
 17. A computer program productcomprising a computer-readable storage medium having computer-readableprogram code portions stored therein, the computer-readable programportions comprising: a first executable portion configured to determinea relationship between nonrecurring costs and potential learning curvevalues; a second executable portion configured to select an uncertaintyvalue from a risk probability distribution associated with nonrecurringcosts; and a third executable portion configured to generate a model ofnonrecurring costs to produce a good based upon the relationship betweennonrecurring costs and potential learning curve values, and theuncertainty value.
 18. A computer program product according to claim 17,wherein the first executable portion being configured to determine arelationship between nonrecurring costs and potential learning curvevalues includes being configured to establish a plurality ofnonrecurring costs values associated with different learning curvevalues, and fit a curve to define the relationship between nonrecurringcosts values and potential learning curve values.
 19. A computer programproduct according to claim 17, wherein the second executable portionbeing configured to select an uncertainty value includes beingconfigured to repeatedly select different uncertainty values, andwherein the third executable portion being configured to generate amodel of nonrecurring costs includes being configured to generate amodel of nonrecurring costs for each selected uncertainty value.
 20. Acomputer program product according to claim 17, wherein thecomputer-readable program portions further comprise a fourth executableportion configured to generate a model of profitability of the goodbased upon the nonrecurring costs model, recurring costs model and ademand model.
 21. A computer program product according to claim 20,wherein the computer-readable program portions further comprise a fifthexecutable portion configured to forecast a market including beingconfigured to randomly select a predefined number of units of a goodbased upon a market potential probability distribution, wherein thefourth executable portion is configured to generate the model ofprofitability further based upon the forecasted market.
 22. A computerprogram product according to claim 21, wherein the fifth executableportion being configured to forecast a market includes being configuredto repeatedly forecast different markets, and wherein the fourthexecutable portion being configured to generate a model of profitabilityincludes being configured to generate a model of profitability for eachof the forecasted markets.
 23. A computer program product according toclaim 22, wherein the fourth executable portion is configured togenerate a model of profitability for a plurality of potential learningcurve values for each forecasted market.
 24. A computer program productaccording to claim 23, wherein the computer-readable program portionsfurther comprise a sixth executable portion configured to determine alearning curve value including being configured to identify a learningcurve value for each forecasted market such that the profitability ismaximized over the potential learning curve values, and determine alearning curve value such that the mean profitability at each identifiedlearning curve value is maximized over the identified learning curvevalues.